Proceedings of The 20th World Multi-Conference on Systemics, Cybernetics and Informatics (WMSCI 2016)
An Agent-Based Dynamic Model of Politics, Fertility and Economic Development
Zining YANG
Department of Politics and Policy, Claremont Graduate University
Claremont, CA 91711, USA
ABSTRACT
studied, and the linkage between macro constraints and micro
level choices remains undiscovered for POFED. Therefore, it
makes sense to investigate income level, fertility decision, and
education at micro level of human agency, to better understand
how individuals make critical decisions and how they behave.
In addition, it will also be critical to understand how macro
environment impacts individual decision, and the feedback of
individual behavior that subsequently shapes and shifts macro
societal trends and conditions.
In the political economy of development, government policy
choices at a single point in time can dramatically affect a
country’s development path by impacting fertility, economic
and political decisions across generations. Combining system
dynamics and agent-based modeling approaches in a complex
adaptive system, a simulation framework of the Politics of
Fertility and Economic Development (POFED) is formalized to
understand the relationship between politics, economic, and
demography change at both macro and micro levels. First, a
new political capacity measurement is used; and the system
dynamics model is validated with the latest data. Second, the
endogenous attributes are fused with non-cooperative game
theory in an agent-based framework to simulate the interactive
political economic dynamics of individual intra-societal
transactions. Finally, macro and micro levels are connected with
policy levers of political capacity and political instability by
merging system dynamics and agent-based components. This
paper also explores the agent-based model’s behavioral
dynamics via simulation methods to identify paths towards
economic development and political stability. This model
demonstrates micro level human agency can act, react and
interact, thus driving macro level dynamics, while macro
structures provide political, social and economic environments
that constrain or incentivize micro level human behavior.
2. POFED BACKGROUND
For many decades, there have been contradictory findings in
studies of the political economy of growth, exploring the factors
that lead to either steady growth or a poverty trap, including
political factors, demographic factors, social and economic
factors. Scholars argue demographic change has significant
impact on economic growth, with fertility rate and human
capital as the two most important attributes [12][13]. Besides
demographic patterns, political factors are also playing a critical
role in a country’s growth path. For example, Feng et al. [11]
argues political freedom is capable of producing sustainable
long-run economic growth once an identified threshold is
exceeded. Even a one-time change in the political environment
affects economic factors over many generations, and the
political condition can be captured via a few critical variables
like political stability and political capacity [12][13].
Keywords: Complex Adaptive Systems, Agent-Based Model,
System Dynamics, Game Theory and Development.
Feng et al [13] presents a formal model that characterizes the
two faces of development—persistent poverty, and
industrialization and rising incomes, and establishes that the
interaction between politics and economics determines which
path a nation travels. In one of the latest POFED literature,
Abdollahian et al. [1] emphasizes the dynamic interrelationships
between income, fertility, political effectiveness, and social
stability. For example, fertility change is impacted by income;
while income depends on past income and political conditions.
There is generational feedback on the creation of human capital,
while political instability has a temporal feedback and depends
on political capacity. Similarly, political capacity is a function
of per capita income, fertility, and instability. Their work
describes how the five main components work at society level,
which can be empirically tested via two systems of equations,
one at aggregated individual level focusing on human capital,
fertility, and income, and the other at society level focusing on
instability and political capacity.
1. INTRODUCTION
This paper investigates countries’ growth paths under different
economic, political, social, and demographic conditions.
Growth and development has been an important issue in the
field of political economy. Among existing studies, two faces of
development attract considerable attention: one is a poverty trap
with persistent economic stagnation; the other is
industrialization and rising incomes. It is argued that political
development, measured as political stability and political
capacity, is sometimes identified as a cause of economic growth
and fertility decision, but sometimes as a consequence of it
[8][13]. On the other hand, economic development is sometimes
modeled to have an impact on human capital and political
development, but sometimes as a result of fertility decision and
political institution [8][12][13].
The rich literature in this field mostly focuses at macro level.
Countries are used as unit of analysis or specific cases.
Empirical research uses macro structural, society level
variables, like GDP, GDP growth, fertility rate, and literacy rate
among others to test different theories. Each one of these
indicators is the sum of millions of human choices, sampled at
arbitrary annual frequencies from an imperfect data and
population distribution. However, the micro level is very poorly
3. COMPLEX ADAPTIVE SYSTEMS
Rooted in international political economy, POFED is a
quantitative, trans-disciplinary approach to understanding
growth and development through the lens of interdependent
economic, demographic, social and political forces at multiple
scales, from individuals to institutions and society as a whole.
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Proceedings of The 20th World Multi-Conference on Systemics, Cybernetics and Informatics (WMSCI 2016)
This paper extends previous work by Abdollahian et al.’s [1]
system dynamics representation of POFED at the societal level
towards integrated macro–micro scales in an agent-based
framework. As macroscopic structures emerging from
microscopic events lead to entrainment and modification of
both, co-evolutionary processes are created over time. Quek et
al. [22] also design an interactive macro–micro agent-based
framework, which they call a spatial Evolutionary Multi-Agent
Social Network (EMAS), on the dynamics of civil violence. A
new approach is proposed where agency matters: individual
game interactions, strategy decisions and outcome histories
determine an individual’s experience. These decisions are
constrained or incentivized by the changing macroeconomic,
demographic pattern, social and political environment via
POFED theory, conditioned on individual attributes at any
particular time. Emergent behavior results from individuals’
current feasible choice set, conditioned upon macro
environment. Conversely, progress on economic development,
the level of internal instability, and population structure emerge
from individuals’ behavior interactions.
for any given society. Individual decisions are affected by other
individuals, social context, and system states. These elements
have first and second order effects, given any particular system
state or individual attributes. Such an approach attempts to
increase both theoretical and empirical verisimilitude for key
elements of complexity processes, emergence, connectivity,
interdependence and feedback found throughout several
disciplines across all scales of development. Figure 1 depicts
the high-level process and multi-module architecture. There are
three modules in the agent-based model: micro agent process,
macro society process, and heterogenous evolutionary game
process.
In order to create a robust techno-social simulation [26]
platform, first a system of coupled nonlinear difference
equations that capture the core logic of POFED macro-social
theory is instantiated. Following Abdollahian et al [2-4]
approach, the following equations are empirically validated
using updated real data: fertility, income, and human capital
from World Bank [28], instability and political capacity from
Kugler and Tammen [17].
Fig. 1. POFED Agent-Based Model Architecture
The design of the micro agent process module incorporates
system dynamics, which allows each individual agent to behave
as a system. Traditional approaches in political science are
static thus cannot capture the dynamic feedback loops that
reflect real-worlds complexity, assuming time plays no role.
System dynamics models can be used when behavior of the
system changes over time and is statistically significant. This
module maintains individual agent variable relationships and
changes following the latest POFED literature [1]. These
endogenously derived individual agent variables impact how
economic transaction games occur, based on society variables
either increasing or decreasing individual wealth and ultimately
societal productivity [7]. Agents are created by adjusting the
mean and standard deviation of fertility, income, and human
capital at the society level. Each individual agent carries all
three variables that are randomized from the society’s
distribution. At the beginning of this process, agents are
allowed to give birth to new agents based on their fertility
attribute. Empirically validated parameter values from Three
Stage Least Square estimation are used as a good first
approximation. This method has been widely used by many
scholars in recent work [2-4] to simulate the dynamic process at
individual level. In this module, feedback is used to model
individual and social phenomena. The value of system dynamic
component is tied to the extent that constructs and parameters
represent actual observed project states. This component helps
facilitate human understanding and communication, and is more
accurate to model time-based relationships between factors and
simulate a system continuously over time.
where b indicates fertility, y indicates income, s indicates
instability, h indicates human capital, and x indicates political
capacity.
Then the POFED endogenous system of agent attribute changes
is fused with a generalizable, non-cooperative Prisoner’s
Dilemma game following Axelrod [5-7], Nowak and Sigmund
[20][21] to simulate intra-societal spatial economic transactions.
Understanding the interactive political effects of macro-socio
dynamics and individual agency in intra-societal transactions
are key elements of a complex adaptive systems approach.
Finally, the model’s behavioral dynamics is explored via
simulation methods to identify paths and pitfalls towards
economic, social, demographic and political development as
well as societal cooperation across different stages of
development. Strong interactions with interdependent strategies
and local social co-evolution [16] help determine global-macro
development outcomes in a particular society.
4. POFED IN AN AGENT-BASED FRAMEWORK
An agent-based model is proposed in a complex adaptive
system framework that captures both macro level changes and
micro level behavior by incorporating system dynamics
component and game theory component. Following the work by
Abdollahian et al [2-4], this model has both the interactive
effects and feedbacks between individual human agency as well
as the macro constraints and opportunities that change over time
Similar to micro agent process, system dynamics technique
is also used in macro society process. Instead of taking each
individual agent as a system, this module takes the entire
society as the system, with political instability, political
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Proceedings of The 20th World Multi-Conference on Systemics, Cybernetics and Informatics (WMSCI 2016)
capacity, economic condition, human capital, and fertility rate
as main attributes. This module is critical as it connects micro
individual level and macro society level. Society economic
condition is aggregated from individual wealth by taking the
mean. Human capital and fertility rate are also calibrated in the
same way. The feedback loop is completed in the way that
initial individual variables are randomized from the society
distribution, get updated in micro agent process and
evolutionary game process, then get aggregated at society level
and interact with other society variables, while society variables
impact the evolutionary game process. Empirically validated
parameter values from Three Stage Least Square estimation are
also used in this process. The updated instability attribute is
brought into the evolutionary game process to affect the
probability that agents interact with each other. This feedback
loop is extremely helpful when studying how individual
behavior changes macro environment, and how environment in
turn impacts individual behavior.
impacts individual decision and capital accumulation. In an
unstable environment, people have less incentive to conduct
economic activities, so the probability of playing a socioeconomic transaction game is low in such condition. When
political instability is low, people are more likely to interact
with each other so the probability is high. The multiplication of
the two probabilities determines the probability that the source
agent plays the transaction game with the target agent. After
each source agent calculates its probability of playing a game
with all possible target agents, it chooses the target with the
highest probability to be its partner. The target agents also
conduct the same process symmetrically for the success pairing.
Once two agents are paired, they choose strategies based on |hihj|. Siero and Doosje [23] among others show that messages
close to a receiver’s position has little effect, while those far
from a receiver’s position is likely to be rejected. So when the
difference of human capital is small, there is a high probability
of playing cooperate while long distance results in high
probability to defect. The relative payoff for each agent is
calculated based on simple non-cooperative game theory
[24][20][10] where T>R>P>S, with T= 2, R=1, P = 0 and S= -1.
When both agents cooperate, they both gain TT; when one
plays cooperate but the other plays defect, the cooperating one
loses while the defecting one gains ST; when both play defect
they don’t gain anything from the transaction PP.
Evolutionary game theory provides insights into understanding
individual, repeated societal transactions in heterogeneous
populations [14][24]. Social co-evolutionary systems allow
each individual to either influence or be influenced by all other
individuals as well as macro society [24][29][25], perhaps
eventually becoming coupled and quasi-path interdependent.
This work does not have well mixed populations, but explicit
spatial contact networks given population density, technology
diffusion and agent attributes. It can be explicitly recognized
that the differential impact of heterogeneous, spatial structures
matters. This captures various individual preferences and their
socioeconomic attributes.
Non-cooperative Aij game is set up, whose outcomes impact
agent yi values for the next iteration. A random value between [0.1, 0.1] is used to model different potential deal sizes, costs,
benefits, or synergies of any social interactions, following
Abdollahian et al. [2-4]. Socio-economic transaction games can
produce either positive or negative values, which allows the
model to capture behavioral outcomes from games with both
upside gains or downside losses. Subsequently, Aij games’ Vij
outcomes condition agent
values, modeling realized costs
Prisoner’s Dilemma is conducted in the evolutionary game
process. Variable talkspan is used to control spatial proximity
interactions, ranging from 1 to 20, defining the grid size radius
for the local neighborhood. At talkspan of 1, agents only
interact and calculate probability of playing the transaction
game with direct neighbors, while at 20, agents can potentially
interact up to 1200 neighbors. To model communications and
technology diffusion for frequency and social tie formation
[18], this module has agent i evaluate the likelihood of
conducting a socio-economic transaction with agent j based on
similarity of income level, stability of the environment, and
physical distance. This approach reflects recent work on the
importance of both dynamic strategies and updating rules based
on agent attributes affecting co-evolution [16][19][3][4].
or benefits from any particular interaction. The updated
=
+ Aij game payoff for each agent then goes into the next
iteration, in which individual endogenous process is repeated,
aggregated up to society as a whole with game processes for t+n
iterations, where n is the last iterate. Ai strategies are adaptive,
which affect Aij pairs locally within an approximate radius as
first order effects. Other agents, within the society but outside
the talkspan radius, are impacted through cascading higher
orders. Agent interaction therefore captures co-evolutionary
behavior in a simple yet elegant manner. Although easily done,
this work specifically does not model mathematically complex,
individual agent memory or learning from Vij outcomes
[5][6][24][3] for simplicity. However, memory and history still
matters. The sum of all prior individual system dynamics
behavior and evolutionary through iterations, does contribute to
each individual and societal current states.
At every time step, 50% of the agents are chosen to be sources
that can choose a target partner; and the remainder agents to be
chosen based on symmetric preference rankings but asymmetric
proximity distributions. Social Judgment Theory [9][15]
describes how the positions of two agents can be conceived
along a Downsian ideological continuum [11] and distance
between these positions affects the likelihood of one accepting
the other’s position. Source agents evaluate the average y
between themselves and all target agents within a given
neighborhood radius. Smaller income difference increases the
probability that Aij will enter into a socio economic transaction
and play a non-cooperative game. This is the first probability
that will impact the choice of target.
As an initial effort at a scale-integrated framework, the design
of three modules allows the study to focus on the coupling of
structure and agency first, before enriching subcomponent
process detail. Thus agents simultaneously co-evolve as strategy
pair outcomes at t to increase y at t+1, thus driving both positive
and negative h, b and y feedback process through t+n iterations.
These shape Ai attributes, which allows adaptation to a changing
environment with aggregated yi, bi, and hi values. Feedback into
subsequent Aij game selection networks and strategy choice
yields a complex adaptive system representation across multiple
scales.
The second probability that goes into the calculation come from
society attribute, instability, measured as the proportion of a
country’s physical capital destroyed in antigovernment violence
[8]. As discussed in literature [12][13][1], political instability
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much stronger than that of instability. Talkspan spatial
proximity is also positive and significant (β = 0.1071),
confirming priors that increasing technology and compressing
potential social space also accelerate development processes.
Increasing individual agents’ ability to reach other like-minded
agents spurs cooperation dramatically based on first order local
interactions. This impact is even greater than that of
cooperation, suggesting technology development provides the
sufficient condition for individuals to interact and create
economic value. Time is slightly negative (β = -0.0411),
indicating that economic prosperity is not self-reinforcing.
Model fit (R2=0.5432) is acceptable given the highly complex
and non-linear dynamics and pooled nature of sensitivity
analysis data. Compared to baseline model, adding individual
choice of cooperative strategy doubles the explanatory power.
In other words, this model captures the micro level behavior
that can better explain macro level phenomena.
5. RESULTS
The agent-based model is implemented in NetLogo [27]. The
entities that interact are all individual agents. The baseline
initial population is 500 to represent a sample of any given
society. State variables are fertility decision, education, and
income. Global variables are level of instability and relative
political capacity, which are setup at society level. Since society
variables do not change on daily basis, the model approximates
one time step as one month given data calibration [3][4] for a
simulated time span of 20 years, which is appropriate for a
cycle in the study of political economy. This design allows
studying the dynamics of politics, economics, and demography
of a society with reasonable frequency and length of time.
In order to make generalizable model inferences, a quasi-global
sensitivity analysis is conducted on both input and initial
condition parameters, for over 17,000 runs across 240 time
steps. With income as the dependent variable, the result is
shown in Table 1. Cooperation is measured as the number of
agents who choose to corporate in the socio-economic
transaction game, and defection is the number of agents
choosing to defect. The number of transaction games and the
number of agents in each time step are also tracked and
presented as Game and Population below. The last variable
Time is the number of iterations in each run, distinguishing
each step in each society’s development process.
After confirming the positive impact of cooperative strategy,
model (2) explores the impact of agents choosing to defect at
the same time. In the process of economic development,
defective behavior has strong and negative impact (β = -0.3522),
contrary to the positive impact of number of agents playing
cooperation (β = 2.1699). This suggests that cooperation does
pay higher social dividends on average. Besides, defective
strategy has stronger impact, in comparison to that of instability
(β = -0.2491) and talkspan (β = 0.2275). Model fit (R2=0.5533)
increases marginally than model (1), though both cooperative
strategy and defective strategy significantly impact individual
wealth and society wealth, adding more explanatory power to
macro level dynamics.
Table 1. Sensitivity Test Result
The last columns focus on the number of interactions among
individual agents and how that impacts the level of income.
Unsurprisingly, the number of societal economic transactions
positively influences wealth (β = 0.7777). In the process of
individuals communicating and making deals with each other,
more products and services become available while the cost of
which goes down. This logic at the societal level is well
discussed and empirically tested in globalization literature: in
the process of increased interconnections among countries,
benefits are derived from specialization of products and
services, which outweighs the economic and social costs by
achieving higher efficiency. Compared to the baseline model,
this model contributes to explanatory power at a limited level,
performing worse than the other two models, suggesting only
counting for the number of interactions is not enough, what is
more important is the type of strategy individuals choose when
they interact with each other.
The first column presents the baseline model from POFED
theory with only macro level variables. One can see that about
20% variance of aggregated income is explained by aggregated
fertility rate, human capital, political instability, political
capacity, population, time, and technology, which is presented
as “talkspan”. This model serves for comparison purpose with
the other three models with individual level variables.
6. CONCLUSIONS
Combining system dynamics, agent-based modeling and game
theory in a complex adaptive system, this simulation framework
of the Politics of Fertility and Economic Development
(POFED) explores the relationship between politics, economic
and demography change at both macro and micro levels. The
results first confirm the findings of the POFED theory at macro
level. The extension of micro level agency and feedback loop
provides more explanatory power to economic development.
The number of individual interactions is critical to
development, as more value can potentially be created.
However, besides the quantity of individual interactions, what
matters most is individual agent’s strategic choice when they
Model (1) first confirms POFED theory that negative value of
instability significantly speeds economic development with
substantive effect (β = -0.2269), as people are able to create
more value in a stable environment. As to the impact of
evolutionary games, one can see the number of agents with
cooperative strategy has a significant positive impact (β =
2.3920) in increasing societal economic value, and the impact is
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play socio economics transaction games. Cooperation pays
higher social dividends on average. Individual’s mutual
cooperative behavior creates trust, which enhances political
stability and economic growth. On the other hand, defective
strategy reduces social wealth, in addition to its negative impact
on the level of trust in the society. Consistent with the findings
from the macro POFED model, the model with micro inputs
also shows increasing technology and compressing potential
social space speed development processes. Macro level
variables also feed back to individual agents updating their
attributes and change the pace and tempo of socio-economic
transactions, which reinforce national development and
economic growth. In terms of model fit, adding individual
choice of strategies increases model fit by doubling that of the
baseline model in which only macro inputs are taken into
account. In other words, this approach that combines both levels
captures the micro level behavior that can better explain macro
level phenomena.
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This innovative approach creates a baseline for current policy
efforts, showing when and how instability or sustainable growth
is likely to occur. Policy can then be tested compared to
baseline outcomes, under normal and crisis scenarios, to assist
in robust policy development. The strength of agent-based
model is its ability to model interactions between individual
agents and the environment, as well as emergent behavior and
complexity of the entire system. The key benefit is
understanding how macro structural environments change and
constrain or incent individual micro-level behaviors, and how
micro interactions shape macro structures.
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